29 research outputs found
A Unifying Framework for Strong Structural Controllability
This paper deals with strong structural controllability of linear systems. In
contrast to existing work, the structured systems studied in this paper have a
so-called zero/nonzero/arbitrary structure, which means that some of the
entries are equal to zero, some of the entries are arbitrary but nonzero, and
the remaining entries are arbitrary (zero or nonzero). We formalize this in
terms of pattern matrices whose entries are either fixed zero, arbitrary
nonzero, or arbitrary. We establish necessary and sufficient algebraic
conditions for strong structural controllability in terms of full rank tests of
certain pattern matrices. We also give a necessary and sufficient graph
theoretic condition for the full rank property of a given pattern matrix. This
graph theoretic condition makes use of a new color change rule that is
introduced in this paper. Based on these two results, we then establish a
necessary and sufficient graph theoretic condition for strong structural
controllability. Moreover, we relate our results to those that exists in the
literature, and explain how our results generalize previous work.Comment: 11 pages, 6 Figure
A Unifying Framework for Strong Structural Controllability
This article deals with strong structural controllability of linear systems. In contrast to the existing work, the structured systems studied in this article have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices, whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests of certain pattern matrices. We also give a necessary and sufficient graph-theoretic condition for the full rank property of a given pattern matrix. This graph-theoretic condition makes use of a new color change rule that is introduced in this article. Based on these two results, we then establish a necessary and sufficient graph-theoretic condition for strong structural controllability. Moreover, we relate our results to those that exist in the literature and explain how our results generalize previous work.</p
A Vector Matroid-Theoretic Approach in the Study of Structural Controllability Over F(z)
In this paper, the structural controllability of the systems over F(z) is
studied using a new mathematical method-matroids. Firstly, a vector matroid is
defined over F(z). Secondly, the full rank conditions of [sI-A|B] are derived
in terms of the concept related to matroid theory, such as rank, base and
union. Then the sufficient condition for the linear system and composite system
over F(z) to be structurally controllable is obtained. Finally, this paper
gives several examples to demonstrate that the married-theoretic approach is
simpler than other existing approaches
Strong Structural Controllability of Signed Networks
In this paper, we discuss the controllability of a family of linear
time-invariant (LTI) networks defined on a signed graph. In this direction, we
introduce the notion of positive and negative signed zero forcing sets for the
controllability analysis of positive and negative eigenvalues of system
matrices with the same sign pattern. A sufficient combinatorial condition that
ensures the strong structural controllability of signed networks is then
proposed. Moreover, an upper bound on the maximum multiplicity of positive and
negative eigenvalues associated with a signed graph is provided